Topics
12. Geometry
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AustraliaNSW
Stage 3

12.02 Circles

Lesson
Practice
Lesson

Are you ready?

Let's review the  properties of shapes  to help us in this lesson.

Examples

Example 1

Does a circle have straight or curved edges?

A
Straight
B
Curved
Worked Solution
Create a strategy

Use the fact that a straight edge goes from one vertex to another without any bends and a curved edge has a bend.

Apply the idea

A circle has no straight edges, and it only has curved edges. So, the correct answer is Option B.

Idea summary

An edge of a shape may be straight or curved. Squares, rectangles and triangles have straight edges. A circle has a curved edge.

Features of circle

Let's learn how to identify the features of circles.

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Examples

Example 2

Consider the circle below:

A circle with a diameter of 8 millimetres and a radius of 4 millimetres.
a

What is the diameter of the circle?

Worked Solution
Create a strategy

Look for the length of the straight line that goes through the centre of the circle and touches opposite points on the edge of the circle.

Apply the idea

The horizontal line touches opposite points on the circle's edge and goes through the centre, so it is a diameter. It's length is 8 mm.

\displaystyle \text{Diameter}\displaystyle =\displaystyle 8 \text{ mm}
b

What is the the radius of the circle?

Worked Solution
Create a strategy

Look for the length of the straight line that goes from the centre of the circle to the circumference of the circle.

Apply the idea

The vertical line goes from the centre of the circle to the circumference of the circle, so it is a radius. It's length is 4 mm.

\displaystyle \text{Radius}\displaystyle =\displaystyle 4 \text{ mm}
Idea summary

Circles have some important features, such as the radius, diameter and circumference. We can use these features, and others, to identify sectors, semi-circles, and quadrants.

  • The circumference is the edge of the circle.

  • The radius is the distance from the centre of the circle to the circumference.

  • The diameter is the distance from one side of the circumference to the other, that passes through the centre.

Outcomes

MA3-15MG

manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

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